If you can't taste a difference then it doesn't make a difference. ;)

The argument for not reboiling water, as -pH said, is that the dissolved oxygen level in the water will be significantly decreased, which will affect the taste. (My suspicion is that the oxygen reacts with compounds to form oxygen-including functional groups on the tea compound, thus increasing its polarity and its solubility as a result. This is similar to how your body deals with some nonpolar chemicals.)

But if you don't use the water for a long enough period of time (how long? I don't know and I'm too lazy to model it if no one's telling me to do it...), then eventually the DO level will return back to an acceptable level (although not necessarily the level it was at when it was first poured -- a lot of faucets have low flow aerators, which would lead to water that is supersaturated with DO).

tl;dr: chemistry